Question

A child makes a poster on a chart paper drawing a square ABCD of side 14 cm. She draws four circles with centre A, B, C and D in which she suggests different ways to save energy. The circles are drawn in such a way that each circle touches externally two of the three remaining circles (in the following figure). In the shaded region she write a message 'Save Energy'. Find the perimeter and area of the shaded region.
(Use $(\pi=\frac{22}{7})$)​

Answer 1

Answer:

The Perimeter of the shaded portion is  44 cm and area of the shaded portion is 42 cm²

Step-by-step explanation:

Given :  

Side of a square = 14 cm  

Radius of a Circle ,r = Side of a square/2

Radius of a Circle ,r = 14/2 = 7 cm

Central angle, θ = 90°

Perimeter of the shaded portion = 4 × length of the arc having Central angle 90°

= 4 ×  θ/360° × 2πr

= 4 × 90°/360° × 2 × 22/7 × 7

= 4 × ¼ × 44

= 44 cm

Perimeter of the shaded portion = 44 cm

Area of a square = Side²

= (14)² = 196 cm²

Area of a square = 196 cm²

Area of the quadrant of one circle = 1/4πr²

Area of the quadrant of four circles = 4 × 1/4πr² = πr²  

= 22/7 × 7²

= 22 × 7

= 154 cm²

Area of the quadrant of four circles = 154

Area of the shaded portion, A = Area of the square,ABCD – Area of the quadrant of four circles

A = 196 - 154  

A = 42 cm²

Hence, the Perimeter of the shaded portion is  44 cm and area of the shaded portion is 42 cm²

HOPE THIS ANSWER WILL HELP YOU….

Here are more questions of the same chapter :

Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions 14 cm × 7 cm. Find the area of the remaining card board. (Use $(\pi=\frac{22}{7})$).

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Four equal circles, each of radius a, touch each other. Show that the area between them is $\frac{6}{7} a^{2}$ (Take $(\pi=\frac{22}{7})$).

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Answer 2

Solution:-

Given :  

Side of a square = 14 cm  

Radius of a Circle = Side of a square/2

=) Radius of a Circle = 14/2 cm = 7 cm

Perimeter of the shaded portion = 4 × length of the arc

=) 4 ×  θ/360° × 2πr

=) 4 × 90°/360° × 2 × 22/7 × 7

=) 4 × ¼ × 44

=) 44 cm

Perimeter of the shaded portion = 44 cm

Area of a square = Side²

=) 14²

=) 196 cm²

Now,

Area of the quadrant of one circle = 1/4πr²

=) 1/4 × 22/7 × 7×7

=) 77/2 cm²

Hence,

4(Area of the quadrant) = 154 cm²

Area of the shaded portion = (Area of square) – 4(Area of the quadrant)

A = 196 - 154  

A = 42 cm²